To be a priori (or its contrary, a posteriori) is a property of cognitions. An a priori cognition is independent of experience and even of all impressions of the senses
(B2). Such a cognition is one that our own cognitive power supplies from itself (sense impressions merely prompting it to do so)
(B1). Correlatively, an a posteriori cognition is one which depends either on impressions of senses (which fall short of being experience) or on experience. These cognitions are also called empirical
, having sources in experience.
The kind of a priori cognitions of interest to Kant are those that occur absolutely independent of all experience,
as contrasted with those in which one empirical cognition anticipates another which has not yet occurred (B3).
Within the sphere of a priori cognitions is a division between those which are pure
and those which are not. A pure a priori cognition contains nothing empirical whatsoever . . . mixed in with them
(B3). Kant gives as an example of a mixed a priori cognition the proposition, Every change has a cause
(B3). While the concept cause borrows nothing from experience, the concept change does. [T]he concept of change requires the perception of some existent and of the succession of its determinations; hence, it requires experience
(A41/B58).
As there are several different types of cognitions, there are correspondingly several types of a priori cognitions.
With respect to sensibility, there are two a priori intuitions: space and time. Space and time are presented a priori . . . as themselves intuitions
(B160).
There are three kinds of a priori concepts. The first are the pure concepts of understanding applying a priori to objects of intuition as such,
or categories (A79/B105). These include both twelve root
concepts (categories) and many derivative concepts derivative from them (A81/B107). These are called notions
(A320/B377). The second are more specific concepts which involve the pure image of sensibility
(A320/B377) or schema,
which ties the categories to time and allows them to apply to objects of experience. The third are ideas, concepts of reason framed from notions and surpassing the possibility of experience
(A320/B377).
Judgments are a priori when they have a source independent of experience. Indeed, the general problem of pure reason
is lies in the question How are synthetic judgments possible a priori?
(B19). The a priori judgments whose source is the power of judgment
form a system of principles of pure understanding, most notably the causal principle. Those whose source lies in concepts of reason are defective in one way or another, as shown in the Transcendental Dialectic.
The two characteristics by which a priori judgments can be distinguished from empirical judgments are their necessity and strict universality. (Presmumably, one cannot directly detect their source.) A judgment is necessary just in case what it states cannot be otherwise
(B3), while it is strictly universal when it is thought in such a way that no exception whatever is allowed as possible
(B4). The two are safe indicators of a priori cognition, and they do moreover belong together inseparably
(B4).
the proposition that all change must have a cause(B3). (Note that the latter judgment is not pure, in that it includes a concept, change, which is tied to experience.)
Prior to Kant, German philosophers tended to think of the a priori in terms of the way in which a connection is established by the mind. Thus, Baumgarten in 1739 wrote of a connection between ground and consequent. If one begins with a ground and connects it with its consequent, one cognizes the connection a priori (Metaphysics, §24). Conversely, if one begins with the consequent and connects it with the ground, the connection is a posteriori.
Lambert in 1764 gave it a more extensive treatment. [T]he words a priori and a posteriori reveal in general a certain order according to which one thing in a series is before or after another
(New Organon, §635). Thus the series may be taken from the front
with what is before, or from the back
with what is after (§634). This distinction is then applied to finding propositions, properties, relations, concepts, etc.,
either on the basis of what we find in experience or on the basis of what is not found in experience. This is illustrated by the difference between experiencing something happening, and foreseeing or inferring that it will happen. The extent to which experience is relied upon is a matter of degree, with one extreme being where we have nothing at all to thank experience for
(§637). A priori knowledge is preferred, and it is obtained by acquiring the relevant concepts without taking experience into account
to the greatest extent possible (§645). For the less one is allowed to rely on experience, the further one reaches with cognition, because that from which something else can be derived is always higher and more universal, or at least cannot be lower and more limited
(§643).
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